What Is the Kelly Criterion? Formula for Position Sizing

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The Kelly criterion is a formula that sets the size of each bet or trade as a fraction of your capital, chosen to maximize the long-run growth rate of that capital. It takes two inputs, the probability of winning and the ratio of average win to average loss, and returns the percentage of your bankroll to commit. A positive result means you have an edge worth sizing. A zero or negative result means the formula says not to take the trade at all.

Where the Kelly Criterion Comes From

John L. Kelly Jr. published the formula in 1956 while working at AT&T’s Bell Laboratories, as part of work on information theory describing how a gambler with a noisy private signal could grow money at the fastest possible rate. Bettors applied it to horse racing soon after, and the mathematician Edward Thorp later used it for blackjack and then in investment management.

The core idea is that growth compounds. Betting too little leaves growth on the table. Betting too much means a run of losses shrinks the account so far that later wins cannot rebuild it. Kelly identifies the fraction between those two outcomes that gives the highest expected logarithmic growth.

The Kelly Criterion Formula

For trading, the formula is usually written as:

K = W − (1 − W) / R

• K: the fraction of capital to commit to the trade.
• W: the probability that a trade is profitable.
• R: the win/loss ratio, meaning the average gain on winning trades divided by the average loss on losing trades.

In betting, the same idea appears as f = (bp − q) / b, where b is the net odds received (a $1 stake winning $2 has b = 2), p is the win probability and q = 1 − p. Setting b equal to R gives the trading form.

Estimating W and R

Both inputs normally come from your own record, such as your last 50 or 60 trades. W is the share that closed with a profit. R is the average profit per winning trade divided by the average loss per losing trade. A backtest can supply the same figures for a strategy without live history, though backtested results tend to flatter real execution.

Worked Example

Hypothetical example, for illustration only. A forex trader reviews 60 closed trades: 33 were winners (W = 0.55). The average winner made $150 and the average loser cost $100, so R = 1.5.

K = 0.55 − (0.45 / 1.5) = 0.55 − 0.30 = 0.25

Full Kelly says to commit 25% of capital per trade. With a $10,000 account, that is $2,500.

What “commit” means matters here. The betting formula assumes the whole stake is lost on a losing bet. A trade with a stop-loss loses only the distance to the stop, so the Kelly fraction is best read as the amount at risk, not the position’s notional value. Here, the trader sizes the position so that hitting the stop-loss costs $2,500, and a position size calculator converts that risk into lots for a given stop distance. On a leveraged account, notional exposure can be many times the amount at risk, which is how oversized Kelly bets turn into a margin call.

Interpreting the Result

• K ≤ 0: no edge on these estimates. If W = 0.40 and R = 1.2, K = 0.40 − 0.60 / 1.2 = −0.10, so the trade should be skipped.
• Small positive K: a thin edge that justifies only small positions.
• Large K: a strong measured edge, or more often an estimate built on too few trades. A result above 100% would imply using leverage, so capping or fractioning the output is standard.

Full Kelly vs. Fractional Kelly

“Full Kelly” means betting the exact fraction the formula gives. “Fractional Kelly” means betting a set share of it, such as half Kelly (0.5K) or quarter Kelly. In the standard model, half Kelly captures roughly three quarters of the full-Kelly growth rate with about half the volatility. Betting more than Kelly adds risk and lowers growth; at around twice the Kelly fraction, expected growth falls to zero, and beyond that it turns negative. Because real estimates of W and R are uncertain, undersizing costs far less than oversizing, which is the main reason traders scale the result down.

Limitations of the Kelly Criterion

• Estimation error. The formula treats W and R as known. A sample of 50 trades can easily overstate an edge, and an inflated W pushes K into the overbetting zone.
• Stable conditions assumed. Kelly assumes each trade is independent and drawn from the same odds. Markets change, and a strategy’s win rate can drift.
• Fixed payoffs. Trades rarely win or lose a set amount. Slippage, gaps through stops and fat-tailed returns (see skewness) mean real losses can exceed the average loss used in R.
• Single-bet focus. The simple formula sizes one opportunity at a time and ignores correlation between open positions. Several Kelly-sized trades on correlated currency pairs can stack into one oversized bet.
• Drawdowns. Even with correct inputs, full Kelly can produce drawdowns that most traders, and most prop firm rules, will not tolerate.
• Personal constraints. Real investors face limits on capital, time horizon and risk tolerance, so some economists prefer expected utility theory, which sizes bets to maximize the expected benefit to a specific person.

What Kelly Is Not

Kelly is sometimes confused with the Martingale strategy, but they work in opposite directions. Martingale increases the stake after losses to recover them. Kelly bets a fixed fraction of current capital, so position size automatically shrinks after losses and grows after wins. Kelly also differs from a flat “risk 1% per trade” rule: a fixed-percentage rule is a chosen risk limit, while Kelly derives the percentage from the measured edge. Nor is it related to Black-Scholes, which values options contracts rather than sizing positions.

The Bottom Line

Traders sizing positions from a measured edge can use Kelly to see whether a strategy justifies risk at all and how much. Because estimates of win rate and win/loss ratio are uncertain, a fractional Kelly applied to the amount at risk, with attention to correlated positions and drawdowns, is the safer practical choice.